Yet another indication of Zuckerberg's interest in public office is a leaked August 2015 email from Facebook COO Sheryl Sandberg to former Hillary Clinton campaign chairman John Podesta.

In the email, which was published by Wikileaks, Sandberg asks Podesta to meet with Zuckerberg. She said that Zuckerberg had been "meeting with people to learn more about next steps for his philanthropy and social action."

"As you may know, he's young and hungry to learn — always in learning mode — and is early in his career when it comes to his philanthropic efforts," Sandberg wrote to Podesta.

"He's begun to think about whether/how he might want to shape advocacy efforts to support his philanthropic priorities and is particularly interested in meeting people who could help him understand how to move the needle on the specific public policy issues he cares most about," she continued. "He wants to meet folks who can inform his understanding about effective political operations to advance public policy goals on social oriented objectives (like immigration, education or basic scientific research)."

Zuckerberg would end up announcing his philanthropic fund, the Chan Zuckerberg Initiative, with his wife later that year.

A loophole that lets him serve for more than two years

President Obama and Zuckerberg share a stage during a town hall meeting at Facebook headquarters in 2011. Associated Press

If Zuckerberg did decide to step into public office, he could very well choose be a cabinet member of some kind rather than run for president. His proposal to serve for up to two years without losing control of Facebook is obviously not long enough for a four-year presidential term.

But as TechCrunch noted on Wednesday, Zuckerberg could technically serve in government for more than two years if he still owns at least 30% of the capital shares in Facebook that he had as of June 2016 and discusses it with the company's board of independent directors.

If he owns less than 30% of the capital shares he had in June 2016 and wants to serve for more than two years, he has to get approval from the majority of Facebook's independent directors, according to the company's filing with the SEC.

Facebook did not immediately return a request for comment about Zuckerberg's potential political aspirations.

In his Facebook post explaining his 2017 goal to meet people from every state, Zuckerberg explained how he thinks about the role of technology from a political perspective.

"Going into this challenge, it seems we are at a turning point in history," he said. "For decades, technology and globalization have made us more productive and connected. This has created many benefits, but for a lot of people it has also made life more challenging. This has contributed to a greater sense of division than I have felt in my lifetime. We need to find a way to change the game so it works for everyone."